Mosaic mask of the god Tezcatlipoca, on show in the Moctezuma: Aztec Ruler exhibition at the British Museum. Photograph: Felix Clay

Your face is reflected in the black mirror, but you can't see yourself clearly. Your features swim in and out of view, like a vision in smoke, in one of the eeriest objects (and that's saying something) in this autumn's sensational blockbuster at the British Museum.

It is easy to imagine why mirrors like this, made from a highly polished sliver of the dark mineral obsidian, were coveted by magicians in Renaissance Europe after the conquest of the indigenous American civilisation that made them. There is an occult quality to the image of yourself that materialises for a moment, making you wonder exactly who you are. Did Moctezuma, last ruler of the Aztec empire, suffer that same anxiety when he gazed into his black mirror? It was said he saw disturbing omens there – signs of strangers coming. Premonitions of imminent catastrophe.

The black obsidian mirror captures the mystery and tragedy at the heart of the British Museum's new exhibition. Moctezuma's story is one of absolute power – and abject surrender. The real emotional power of this show comes at the end, when you see the armour and banners of the Spanish soldiers who destroyed this ruler and his world, and are confronted with a detective puzzle. Why did he make it so easy for them?

A true-life epic

The fall of Moctezuma is a fabled chapter in the bloody European road to world conquest and it makes a fitting conclusion to the British Museum's series of exhibitions about great rulers. This series began with the First Emperor of China; it ends with one of the last native rulers of the Americas. The tale it tells – and one of the virtues of this compelling show is that it gives a distant place and time a graspable human narrative – is one of the most haunting of all true-life epics.

In 1519 the Spanish adventurer Hernan Cortés and his 450 men, their minds full of gold, landed on the Mexican coast. As they approached the dominant city of the region, Tenochtitlan, its all-powerful god-king Moctezuma II wondered what to do. In the end he decided to meet the foreigners in peace, give them gifts and invite them to stay. When they suddenly proposed to arrest him, he went along peacefully. His final act was to address his rebellious subjects, who were on the point of finally rising against the vicious intruders, and urge them to keep calm – to be passive like him. He was hit by stones hurled by the vengeful crowd. Three days later he died of his wounds – or so his Spanish captors reported. Evidence presented in this exhibition suggests they simply stabbed him to death when they realised he had become so unpopular that he had no influence on his people, who had so recently all but worshipped him.

Moctezuma is a kind of cross between Tutankhamun and Neville Chamberlain – a splendid king turned craven appeaser. This exhibition doesn't so much overturn that image as complicate, enrich and reframe it, fleshing out the myth, making history from legend.

It gets better and better, from an unnecessarily baffling start. The British Museum in recent years has projected itself as a liberal meeting place of world cultures – rightly, and with hugely popular results. But just occasionally its determination to say the right thing can get a bit prissy and worthy. I find it irritating to come into an exhibition that says on the poster "Moctezuma: Aztec Ruler" only to be met by a towering and very long wall-text firmly explaining that we are no longer to call the Aztecs "Aztecs" at all. Apparently this name was imposed in the early 19th century. The correct name is Mexica. Throughout this show, you are warned, the name Mexica will be used – we shall hear no more of Aztecs! And by the way, it adds, Montezuma, the name by which its hero will be familiar to many, is an English misspelling. From now on it's Moctezuma, thank you very much.

If you don't feel just slightly put upon by this stern lecture, you are probably a Mexica, quietly satisfied that a centuries-old misnaming has been corrected. Myself, I found it distracting and a bit pointless, because we won't pronounce Mexica correctly anyway, any more that we get Michelagnolo's name right, and anyway no one is going to come away from this exhibition thinking cosy thoughts about pre-conquest American cultures. For it soon becomes clear that Aztecs by any other name are just as blood-soaked.

No amount of hand-wringing or good intentions can turn the civilisation the Spanish encountered in 1519 into some benign pre-colonial paradise. When you finally recover from the show's pedantic beginning, one of the first things to catch your eye is a colossal stone eagle with a basin carved out of its back – a receptacle for human blood from sacrifices at Tenochtitlan's Templo Mayor.

And that's just the start of it. Three stone skulls in a row are a sculptural representation of galleries of real skulls of sacrificial victims that towered over the city. Two beautiful pottery vessels also have startling three-dimensional skulls bursting from them. These skulls are painted red and white – brilliantly imitating, points out the catalogue, the bits of bloody fat still clinging to freshly flayed skulls.

If the opening rooms of the exhibition seem a bit fussily correct, the style of presentation soon starts to make sense. The curators make no attempt to disguise or apologise for Mexica human sacrifice. On a model of the city's sacred precinct, they show rivers of blood streaming down the white steps of the great temple. This gift of blood to the gods was necessary to ensure the very survival of nature. Moctezuma ritually wounded himself and gave his own blood when he was crowned in 1502; he then had to lead his army in a "coronation war" whose goal was to provide captives for human sacrifice.

All of this is coolly and – perverse word – sensitively expounded. This is an exhibition that sets out to reconstruct an entire social, political and religious universe around the figure of one man, Moctezuma. It can easily make us study detailed exposition, and listen to a bit of lecturing even, for the fire of Mexica art is so intense that all the anthropological texts serve the usefully cooling function of sour cream with chilli.

A massive carved stone block that to me looks like a throne – but the catalogue describes as a sculpture celebrating sacred warfare – towers at the very heart of the exhibition, directly under the oculus of the Reading Room's dome. Death-faced gods parade on it in a blocky frieze, below a spiky disc representing the sun. It is one of the most rightly renowned Mexica sculptures, a highlight in a storm of fire serpents, feathered gods and shape-shifting warriors that entrances the imagination.

Detail from a portrait of Moctezuma from the Uffizi Gallery, on show in the Moctezuma: Aztec Ruler exhibition at the British Museum. Photograph: Felix Clay

A history cut short

Moctezuma inherited one of the world's richest visual traditions. All the styles of art in this show have origins going back 3,000 years to the age of the Olmecs. Not only the art but the ideas of the Mexica drew on the long history of city states in the region now known as Mesoamerica. Even the complex calendar Moctezuma used can be traced back to the Maya and ultimately the Olmecs. What we see here is a snapshot of a long history just before it was violently cut short – and it was in no sense a world in decline. The Mexica had a special feel for realism, for vivid observation. A gigantic stone snake's tail has a finely observed rattle. A mask's twisting, apparently abstract turquoise decoration turns out on closer inspection to depict two intertwining snakes: as the catalogue points out, this is an accurate portrayal of the way snakes mate. The Mexica looked hard at snakes.

The most moving observations these artists made were of the human face. "Portrayal" is probably a misleading word. There were no "portraits" in this world. The Mexica images of faces are archetypal, but arresting. The grey ashen face of the god Tezcatlipoca held me for a long time. His features carved in smooth greenstone are as lifelike as if it were a clay mask moulded on a real face: the nose with its vivid flanges and strong bone, the lips parted to reveal square teeth. Equally beguiling is the head of an eagle warrior, his bird of prey helmet declaring he belongs to the elite of Moctezuma's army. Hollow eyes gaze from a powerfully accurate human face of a man who has assimilated the strength of an avian raptor.

Which brings us back to the enigmatic story this exhibition tells. If it starts clunkily, it ends brilliantly. Spanish and colonial paintings and objects, and codices – Mexica books – telling the story of the conquest, give a complex and unsettling account of the fall of Moctezuma. Did he really, as the manuscripts here claim, see prodigies in the heavens and other omens of the Spanish attack? Was his paralysis somehow dictated by prophecy, or is that just a European myth?

Moctezuma was a great war leader, and the images of eagle and jaguar warriors and the throne-like image of war itself make it clear how martial Mexica culture was. So what went wrong? In a way, it's obvious. One of the exhibition's most startling objects is a sacrificial dagger. Its handle is fabulously decorated. But its blade is knapped flint – a kind of blade that had stopped being used in the Old World with the passing of the Neolithic. For all the richness of their civilisation – the elaborate calendar and stupendous architecture – the Mexica were literally living in the stone age. They worked gold, but not iron. The steel conquistador breastplate and sword say it all – and that's without the Spanish horses, new to America, and guns.

This exhibition succeeds in revealing a lost world. Moctezuma's passive acceptance of Cortés suggests he simply didn't see the use of fighting. Maybe he was a wise ruler doing his best for his people by urging them not to waste their time against impossible odds. Obviously that was never going to get him a reputation as a Mexican national hero. Anyway, fighting was even more irrelevant than he realised. The Spanish accidentally brought smallpox, which reduced the indigenous population by 90% in a few years. The Mexica feared the end of the world; their rituals tried to hold it off for one more period of 52 years. History's incredible cruelty was written into their beliefs. Moctezuma could see it in his black mirror.

Moctezuma: Aztec Ruler is at the British Museum, London 24 September-24 January. 0207-323 8181, britishmuseum.org